Zeytuna beach isn't a huge beach with a lot of frills. It is just a nice small beach where you can go and relax. It is on an island so you have to take the water taxi from the Sultan Bey Hotel downtown, or walk across the footbridge by the Hill hotel. The beach is nice and sandy and there are plenty of beach chairs with umbrellas that will give you shade and privacy. There is a great volleyball court with an omnipresent camel next to it. You can rent the camel for a negotiatable price if you want, 15 Pounds for a half an hour is fair. There are also a few horses you can rent if you want.
The bar features a good selection of cocktails and has standard beach food, sandwiches and pizza. There are also a few shops where you can buy cheesy tourist fodder or get a chic henna tattoo.
The water at Zeytuna is lovely, crystal clear and a beautiful blue/green. There is a dock that extends way out into the water, and for good reason. About 10 feet out it is deep enough to swim, but past that it is shallow and rocky, so you have to go to the end of the dock if you want to do more than just float in the water. At the end of the dock is a nice diving platform too.
Zeytuna Beach is also the home to a number of nice late night beach parties with authentic Turkish food, a DJ and a bonfire, definitely worth checking out.